AMC 12 2017a Problem 9

Let $S$ be the set of points $(x,y)$ in the coordinate plane such that two of the three quantities $3$, $x+2$, and $y-4$ are equal and the third of the three quantities is no greater than the common value. Which of the following is a correct description of $S$?

\textbf{(A)}\ \text{a single point} \textbf{(B)}\ \text{two intersecting lines} \ \textbf{(C)}\ \text{three lines whose pairwise intersections are three distinct points} \ \textbf{(D)}\ \text{a triangle} \textbf{(E)}\ \text{three rays with a common point}